Consider a solid sphere, determined by the volume x^2 + y^2 + z^2 ≤ r^2 , with a non-uniform density rho(x, y, z) = a|z|. determine the total mass of the sphere in terms of a and r. b) consider a flat disk of radius r, with an areal mass density given by σ(r, θ) = ar^2 sin^2 (θ), where a is a given constant. describe in words and a simple sketch this mass density. then, determine the total mass of the thin disk in terms of a and r.

Which statement best explains why an object weight less on mercury than it does on earth

A33.1 g copper object is launched from a 1.5 m 30° steel incline positioned on the floor by being pulled up a string attached to a 50.0 g mass suspended vertically over a pulley. the object is projected towards a glass table where it lands when it is at the point along its trajectory with the lowest speed. it comes to a halt when it clears the opposite edge of the table. it then falls and lands on 9 physics texts each 5 cm thick that are stacked on the floor on the opposite side of the table. assume that the table does not have a ledge and the rectangular object experiences 0.05 n of air resistance as it falls towards the books. how far and how long did the object travel and how fast does it hit the books. assume that at the moment the copper object leaves the incline, the massless string and ideal pulley break off

Explain what makes a passenger in a turning car slide toward the door. critical thinking